TRAVELING-WAVE TUBES 9 



the phenomena in a traveling-wave tube can be satisfactorily described in 

 a theory which is simple enough to yield useful results. Most analyses, for 

 instance, deal only with the small-signal or linear theory of the traveling- 

 wave tube. The distribution of current in the electron beam can have an 

 important influence on operation, and yet in an experimental tube it is often 

 difficult to tell just what this distribution is. Even the more elaborate analy- 

 ses of linear behavior assume a constant current density across the beam. 

 Similarly, in most practical traveling-wave tubes, a certain fraction of the 

 current is lost on the helix and yet this is not taken into account in the 

 usual theories. 



It has been suggested that an absolutely complete theory of the traveling- 

 wave tube is almost out of the question. The attack which seems likely to 

 yield the best numerical results is that of writing the appropriate partial 

 differential equations for the disturbance in the electron stream inside the 

 helix and outside of the helix. This attack has been used by Chu and Jackson^ 

 and by Rydbeck.^ While it enables one to evaluate certain quantities which 

 can only be estimated in a simpler theory, the general results do not differ 

 qualitatively and are in fair quantitative agreement with those which are 

 derived here by a simpler theory. 



In the analysis chosen here, a number of approximations are made at the 



very beginning. This not only simplifies the mathematics but it cuts down 



the number of parameters involved and gives to these parameters a simple 



physical meaning. In terms of the parameters of this simple theory, a great 



many interesting problems concerning noise, attenuation and various bound- 



' ary conditions can be worked out. With a more complicated theory, the work- 



i ing out of each of these problems would constitute essentially a new problem 



I rather than a mere application of various formulae. 



i There are certain consequences of a more general treatment of a traveling- 

 jwave tube which are not apparent in the simple theory presented here. 

 Some of these matters will be discussed in Chapters XII, XIII and XIV. 



rhe theory presented here is a small signal theory. This means that the 

 I equations governing electron flow have been linearized by neglecting certain 

 I quantities which become negligible when the signals are small. This results 

 ■in a wave-type solution. Besides the small signal Umitation of the analyses 

 '.presented here, the chief simplifying assumption which has been made is 

 ithat all the electrons in the electron flow are acted on by the same a-c field, 

 or at least by known fields. The electrons will be acted on by essentially the 

 same field when the diameter of the electron beam is small enough or when 



- L.J. Chu and J. D.Jackson, "Field Theory of Traveling-Wave Tubes," Froc. I. R. E., 

 \n\. 36, pp. 853-863, July 1948. 



^ Olof E. H. Rvdbeck, "The Theory of the Traveling-Wave Tube," Ericsson Technics, 

 Vo. 46, 1948. 



